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    ABSTRACT: This paper describes the operation of a new design of wave energy converter. The design consists of a buoyant tethered submerged circular cylinder which is allowed to pitch freely about an axis below its centre. Within the body of the cylinder a fluid half fills an annular tank whose shaped inner walls allow the fundamental sloshing mode of the fluid be to tuned to any period of interest. The pitching motion of the cylinder in waves induces a sloshing motion inside the annular tank which in turns drives an air turbine connecting air chambers above the two isolated internal free surfaces. The concept behind this design is to couple resonances of the pitching cylinder with natural sloshing resonances of the internal water tank and thus achieve a broadbanded power response over a wide range of physically-relevant wave periods. Mathematically, the problem introduces new techniques to solve the series of complex internal forced sloshing problems that arise and to efficiently determine key hydrodynamic coefficients needed for the calculation of the power from the device. The results show that practical configurations can be found in which the efficiency of a two-dimensional cylindrical device is close to its maximum theoretical limit over the target range of periods from 55 to 1111 seconds.
    Full-text · Article · Sep 2014 · European Journal of Mechanics - B/Fluids
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    ABSTRACT: We extend to the function field setting the heuristic previously developed, by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments and ratios of L -functions defined over number fields. Specifically, we give a heuristic for the moments and ratios of a family of L -functions associated with hyperelliptic curves of genus g over a fixed finite field FqFq in the limit as g→∞g→∞. Like in the number field case, there is a striking resemblance to the corresponding formulae for the characteristic polynomials of random matrices. As an application, we calculate the one-level density for the zeros of these L-functions.
    Preview · Article · Sep 2014 · Journal of Number Theory
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    ABSTRACT: Continuous action space games are ubiquitous in economics. However, whilst learning dynamics in normal form games with finite action sets are now well studied, it is not until recently that their continuous action space counterparts have been examined. We extend stochastic fictitious play to the continuous action space framework. In normal form games with finite action sets the limiting behaviour of a discrete time learning process is often studied using its continuous time counterpart via stochastic approximation. In this paper we study stochastic fictitious play in games with continuous action spaces using the same method. This requires the asymptotic pseudo-trajectory approach to stochastic approximation to be extended to Banach spaces. In particular the limiting behaviour of stochastic fictitious play is studied using the associated smooth best response dynamics on the space of finite signed measures. Using this approach, stochastic fictitious play is shown to converge to an equilibrium point in two-player zero-sum games and a stochastic fictitious play-like process is shown to converge to an equilibrium in negative definite single population games.
    Preview · Article · Jul 2014 · Journal of Economic Theory
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